Question: The geometric sequence $(a_i)$ is defined by the formula: $a_i = -\dfrac{1}{9} \left(-3\right)^{i - 1}$ What is $a_{5}$, the fifth term in the sequence?
Answer: From the given formula, we can see that the first term of the sequence is $-\dfrac{1}{9}$ and the common ratio is $-3$ To find $a_{5}$ , we can simply substitute $i = 5$ into the given formula. Therefore, the fifth term is equal to $a_{5} = -\dfrac{1}{9} \left(-3\right)^{5 - 1} = -9$.